• 3 Posts
  • 15 Comments
Joined 1 year ago
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Cake day: June 22nd, 2023

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  • I’m kind of dissatisfied with the answers here. As soon as you talk about actually drawing a line in the real world, the distinction between rational and irrational numbers stops making sense. In other words, the distinction between rational and irrational numbers is a concept that describes numbers to an accuracy that is impossible to achieve in real life. So you cannot draw a line with a clearly irrational length, but neither can you draw a line with a clearly rational length. You can only define theoretical mathematical constructs which can then be classified as rational or irrational, if applicable.

    More mathematically phrased: in real life, your line to which you assign the length L will always have an inaccuracy of size x>0. But for any real L, the interval (L-x;L+x) contains both an infinite number of rational and an infinite number of irrational numbers. Note that this is independent of how small the value of x is. This is why I said that the accuracy, at which the concept of rational and irrational numbers make sense, is impossible to achieve in real life.

    So I think your confusion stems from mixing the lengths we assign to objects in the real world with the lengths we can accurately compute for mathematical objects that we have created in our minds using axioms and definitions.



  • I see a lot of hate against the concept of doing one’s own research on the internet and it really bothers me. The problem is not doing one’s own research. The scientists that wrote this paper also did their own research. All scientists (should) do their own research. That’s inherent to science and that’s part of what got humanity this far. The problem is that some people lack the capabilities to properly assess information sources and draw correct conclusions from them. So these people end up with incorrect beliefs. Of course they could just “trust the experts” instead, but how are they supposed to know which experts to trust if they’re not good at assessing sources of information? Finding those experts is in itself a task that requires you to do your own research.

    TL;DR: I think this hate on “doing your own research” is unjustified. People believing nonsense is a problem that is inescapable and inherent to humanity.